Fluctuation Spectroscopy In Granular Superconductors With Application To Boron-Doped Nanocrystalline Diamond

We perform a detailed calculation of the various contributions to the fluctuation conductivity of a granular metal close to its superconducting transition. We find three distinct regions of power law behavior in reduced temperature, eta = (T - T-c)/T-c, with crossovers at Gamma/T-c and E-Th/T-c, where Gamma is the electron tunneling rate, and E-Th is the Thouless energy of a grain. The calculation includes both intergrain and intragrain degrees of freedom. This complete theory of the fluctuation region in granular superconductors is then compared to experimental results from boron-doped nanocrystalline diamond, using the assumption of a constant phase breaking rate tau(-1)(phi). We find a semiquantitative agreement between the theoretical and experimental results only in the case of large phase breaking. We argue that there may be a phase breaking mechanism in granular metals worthy of further experimental and theoretical investigation.